DR = (L − L₀)/L₀ for the sample length L and L₀ (initial value).

      Source: Reproduced from Wang et al., Macromolecules 2017, 44, 3285–3300.

FIGURE 6.14 Temperature dependence of 2D X‐ray diffraction pattern of highly oriented α form under a constant tensile force (about 1 MPa).

      Source: Reproduced from Wang et al., Macromolecules 2017, 44, 3285–3300.

6.4 MICROSCOPICALLY‐VIEWED STRUCTURE‐MECHANICAL PROPERTIES OF PLA

The estimation of the mechanical property of an ideal crystalline state, or the ultimate mechanical property, is important as a guiding principle for the development of PLA samples with excellent mechanical properties. The theoretical prediction of mechanical properties with high reliability can be made for the first time by using the accurate crystal structure information and the credible potential functional parameters, which can reproduce the various kinds of the experimentally obtained physical constants including the vibrational spectroscopic data [61–72]. The 3D elastic constant tensors of PLLA α [5], δ [9] and β forms [20] were calculated using the above‐mentioned X‐ray‐analyzed crystalline structures:

FIGURE 6.15 (a) Comparison of the unit cell ab‐plane structure between the α (δ) and β forms, where the model 2 is employed for the β form. The U and D indicate the upward and downward helical chains along the c axis, respectively. (b) A schematic illustration of the structural transformation model from the α (α′) form to the β form. The set of arrays A, B and A slip along the 110 planes.

      Source: Modified from the reference [20]. Reproduced from Wang et al., Macromolecules 2017, 44, 3285–3300.

      (c) The change of the X‐ray coherent domain size in the transition process from the α to δ to β forms.

      PLLA α form

      Elastic constants matrix,

Compliance tensors matrix,

      PLLA δ form

      PLLA β form

      The calculated Young’s moduli along the c‐axis (E _c = 1/s ₃₃) are compared among the α, δ, and β forms, as shown below:

       α form: E c = 14.7 GPa [66] (X‐ray observed 13.76 GPa [66, 73])

       δ form: E c = 12.5 GPa [66] (X‐ray observed 12.58 GPa [66])

       β form: E c = 15.4 GPa [20]

      The experimental evaluation of the Young’s modulus of the crystal lattice along the chain axis, which is often called the crystallite modulus, was performed using the X‐ray diffraction method [67], where the crystalline strain along the chain axis was measured under constant tensile stresses by assuming the stress working on the